Two-Sided Random Acceptability graph Matching Markets: m 1 Ex-Ante - PowerPoint PPT Presentation

Mar 14, 2024 •94 likes •148 views

Two-Sided Matching Market Two-Sided Random Acceptability graph Matching Markets: m 1 Ex-Ante Equivalence of the w 1 m 2 Deferred Acceptance w 2 Procedures m 3 w 3 m 4 w 4 Simon Mauras m 5 simon.mauras@irif.fr Agents order their neighbours

Two-Sided Matching Market Two-Sided Random Acceptability graph Matching Markets: m 1 Ex-Ante Equivalence of the w 1 m 2 Deferred Acceptance w 2 Procedures m 3 w 3 m 4 w 4 Simon Mauras m 5 simon.mauras@irif.fr Agents order their neighbours uniformly at random. Université de Paris, IRIF Mauras (Université de Paris, IRIF) EC’20 Poster 1 / 4
You are an evil decision maker You need to chose the procedure: • MPDA : Men Proposing Deferred Acceptance • WPDA : Women Proposing Deferred Acceptance You really like this matching: m 1 w 1 m 2 w 2 µ m 3 w 3 m 4 w 4 m 5 What should you do to maximize the probability of chosing µ ? Mauras (Université de Paris, IRIF) EC’20 Poster 2 / 4
Output distribution of MPDA . Output distribution of WPDA . P [ MPDA outputs µ ] = 299 / 5184 P [ WPDA outputs µ ] = 299 / 5184 Mauras (Université de Paris, IRIF) EC’20 Poster 3 / 4
In the proof... Lattice of stable matchings. Theorem. “Ex-ante equivalence” MPDA and WPDA have the same output distribution . If you don’t know the preferences, you cannot “manipulate”... Probability of stability. In the talk/paper: 1 Proof of the Theorem. 2 Non-uniform distributions. Mauras (Université de Paris, IRIF) EC’20 Poster 4 / 4

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